My suggestion is to implement a feature which will auto ping google when a new question is added to the website. The ping can be done using a simple HTTP request, to the sitemap url as a parameter to google webmasters - for example, to

2 Answers

It's kind of pointless to be suggesting to Google that they download your sitemap every time there is a new question. Perhaps once a day would work, but Google will download your sitemap often enough anyway - if you have new pages every day, Google will detect that and crawl your site faster.

Constantly pinging Google won't always make them download your sitemap faster. Plus there are no problems crawling Q2A sites so a sitemap doesn't really add that much anyway!